Kelvin waves are waves (pressure waves or gravity waves, i.e., atmosphere or ocean) formed due to the Coriolis force's effect on a fluid when a barrier is present. For example, coastal Kelvin waves can form near the COAST of an ocean. The equator also effectively forms a barrier, due to the Coriolis force vanishing at the equator, allowing formation of equatorial Kelvin waves.
Equatorial waves also include a type of Rossby wave (equatorial Rossby waves). A difference is that equatorial Kelvin waves move eastward (into the Earth's rotation) and equatorial Rossby waves of one type (long Rossby waves) move westward and of another (short Rossby waves) move eastward. Equatorial waves form part of the mechanism that creates El Niño cycles.
These wave mechanisms affect the atmospheres of other planets (e.g., Jupiter, extra-solar planets).